Apparatus and methods for light beam routing in telecommunication

ABSTRACT

A LCOS routing device, comprising: an optical input and plurality of optical outputs; a spatial light modulator (SLM) between said input and output, for displaying a kinoform; a data processor, configured to provide kinoform data for displaying said kinoform on said SLM. Said data processor inputs routing and calculates said kinoform data. Said data processor calculates kinoform data by: determining an initial phase pattern for said kinoform; calculating a replay field of said phase pattern; modifying an amplitude component of said replay field, retaining a phase component of said replay field to provide an updated replay field; performing a space-frequency transform on said updated replay field to determine an updated phase pattern for said kinoform; and repeating said calculating and updating of said replay field and said performing of said space-frequency transform until said kinoform for display is determined; and outputting said kinoform data for display on said LCOS SLM.

RELATED APPLICATIONS

This application is a continuation of co-pending U.S. patent applicationSer. No. 14/000,203, filed May 8, 2015, entitled Apparatus and methods,which is a national stage entry of PCTGB2012050340, filed Feb. 15, 2012,which claims priority to GB 1102715.8, filed Feb. 16, 2011, the entiredisclosure of which is herein incorporated by reference.

FIELD OF THE INVENTION

This invention relates to methods and apparatus for routing light beamsin telecommunications devices using holographic techniques. Inparticular aspects of the invention relating to displaying kinoforms onLCOS (Liquid crystal on silicon) devices.

BACKGROUND TO THE INVENTION

The use of holographic techniques, in particular kinoforms (phase onlyholograms) in telecommunications presents special problems, inparticular because of the high signal-to-noise (SNR)/low crosstalkrequirements as compared with display applications. For example in adisplay application the level of noise/crosstalk may be of order 1:300whereas in a telecommunications device it may be of order 1:10000. otherspecial problems which can arise are as follows:

-   -   Operation at the long wavelength of 1.5 micron necessitates the        use of thick liquid layers (compared with visible light        devices), making the accurate rendition of the pixel array        pattern in the liquid crystal more difficult.    -   High diffraction efficiency and very low crosstalk are required.    -   Reconfigurable dynamic pixilated kinoforms rendered on LCOS        devices have special problems compared with fixed kinoforms        produced by photolithographic processes. They have a relatively        large pixel size and the size of the pixel array is limited and        they suffer from artefacts related to the liquid crystal layer.    -   In some cases relatively fast computation of pixel patterns is        required e.g. to adaptively adjust beams or the configure new        switch configurations.

Background prior art can be found in U.S. Pat. No. 5,617,227; U.S. Pat.No. 5,416,616; WO03/021341; U.S. Pat. No. 7,457,547; and “Iterativealgorithm for the design of diffractive phase elements for laser beamshaping”, J. S. Liu and M. R. Taghizadeh, Aug. 15, 2002, Vol. 27, No.16, OPTICS LETTERS p. 1463; “Hologram Optimisation Using Liquid CrystalModelling”, Georgiou A. G. et al., Molecular Crystals and LiquidCrystals 2005 vol 434 pp 511-526; and “Fresnel ping-pong algorithm fortwo-plane computer-generated hologram display” in 10 Feb. 1994/Vol. 33,No. 5/APPLIED OPTICS pp. 869).

SUMMARY OF THE INVENTION

According to the present invention there is therefore provided a LCOS(liquid crystal on silicon) telecommunications light beam routingdevice, the device comprising: an optical input; a plurality of opticaloutputs; a LCOS spatial light modulator (SLM) in an optical path betweensaid input and said output, for displaying a kinoform; a data processor,coupled to said SLM, configured to provide kinoform data for displayingsaid kinoform on said SLM; wherein said kinoform data defines a kinoformwhich routes a beam from said optical input to a selected said opticaloutput; wherein said data processor is configured to input routing datadefining said selected optical output and to calculate said kinoformdata for routing said beam responsive to said routing data; and whereinsaid data processor is configured to calculate said kinoform data by:determining an initial phase pattern for said kinoform; calculating areplay field of said phase pattern; modifying an amplitude component ofsaid replay field to represent a target replay field for said beamrouting, retaining a phase component of said replay field to provide anupdated replay field; performing a space-frequency transform on saidupdated replay field to determine an updated phase pattern for saidkinoform; and repeating said calculating and updating of said replayfield and said performing of said space-frequency transform until saidkinoform for display is determined; and outputting said kinoform datafor display on said LCOS SLM.

In embodiments, using the above described procedure enables real timekinoform calculation, even in a system with a large number of outputsand/or where the hologram has a large number of pixels. For example thekinoform may be calculated in a few tens of milliseconds, particularlywhere the space-frequency transform is implemented as a hardware fastFourier transform. Embodiments of the procedure also facilitate theapplication of various additional techniques for reducing crosstalk andimproving the signal-to-noise ratio, which is important fortelecommunications.

Thus in one preferred embodiment the data processor is configured tomodify the phase pattern of the kinoform in response to data defining amodel of a response of the LCOS spatial light modulator prior tocalculating the replay field of the phase pattern. Broadly speaking,this enables a rapid calculation to be performed in which the responseof a physical liquid crystal material is modelled so that the non-idealresponse can be corrected in one or more subsequent iterations of thekinoform calculation procedure. This facilitates more accurateinformation and crosstalk reduction. A procedure for compensating for aphase response of a liquid crystal is described in Georgio et al (ibid),and such a procedure may be used here.

Embodiments of the kinoform calculation procedure also enable‘overcompensation’ of the target replay field to which the calculatedreplay field is modified, the overcompensation being such that theiterative kinoform determination process converges faster than it wouldotherwise. This can be achieved by adjusting the amplitude component ofthe target replay field, for example using the procedure described inLiu et al (ibid), using a modified fourier-domain constraint function,discussed further in “Symmetrical iterative Fourier-transform algorithmusing both phase and amplitude freedom for the design of diffractivebeam shaping elements”, Lui et al., 2005 Conference on Lasers andElectro-Optics Europe, SPIE, at page 610. In embodiments of theprocedure the calculated amplitude component of the replay field isreplaced by the desired (amplitude) replay field, but in otherapproaches the calculated replay field may simply be modified to moreaccurately represent the desired, target replay field.

The kinoform calculation procedure also enables redistribution of noise,spatially in the replay field, away from the selected output. Forexample this may be achieved by expanding the replay field used in theiterative kinoform calculation procedure so that it is greater than theactual replay field used by the routing device. The actual replay fieldmay be defined by a perimeter defined by the plurality of opticaloutputs, in the replay field, but if a larger target replay field isused for the kinoform calculation then the replay field noise is spreadout over this larger area, thus reducing the noise in the portion of thereplay field actually used in the device (the skilled person willappreciate that, in embodiments, the optical outputs may be defined by aset of optical fibre inputs to optical fibres which lead away from thedevice). More particularly, the “don't care” area may comprise all theoutput field other than the optical outputs. This is a considerableadvantage compared to the case of holographic projection for displaypurposes. In practical implementation there is a balance between thesize of the replay field used in the calculation and the time taken forthe calculation (and also the termination point of the iteration, whichwill generally be when the average error is less than a thresholdlevel).

In embodiments of the device one or more of the optical outputs may bemonitored to determine an optical signal level, and then the targetreplay field may be adjusted, responsive to this, to optimise a couplingbetween the routed beam and an optical output. For example the overlapintegral between the replay field and optical output (fibre optic input)may be maximised. This may, for example, be performed as a calibrationprocedure and/or in response to changes in temperature or time, forexample at intervals. Optionally more than one such replay fieldcalibration may be employed for more than one temperature range, inwhich case the device may include a temperature sensor to select therange/calibration. It will be recognised that since in general theoutput ports will have very similar responses, only one output port needbe monitored and ‘calibrated’ in this way to determine a ‘calibration’for the device.

In further embodiments the calculation of the kinoform/replay field mayinclude modifying the amplitude component of the target replay field tocompensate for an envelope amplitude variation in the replay field. Thisis typically a sinc function in two dimensions, resulting from the lightdiffraction atom of an individual pixel of the LCOS SLM. For example theamplitude of a beam deflected to a central portion of the replay fieldmay deliberately be attenuated so that the amplitude of the beam whendirected to a portion of the replay field away from the centre or opticaxis has a similar or substantially the same amplitude.

Embodiments of the device may incorporate channel attenuation and/orequalisation, for example by modifying the desired target replay fieldto modify the desired amplitude of an output beam. The ability tocontrol the attenuation of a beam in a telecommunications device is animportant advantage.

In embodiments a plurality of inputs rather than just a single input maybe provided, and in a general case, n input beams may be mapped to noutput beams.

Either or both of an input and output to the device may bebi-directional. The skilled person will appreciate that the inputs andoutputs may be exchanged so that the invention also provides, inembodiments an n to 1 multiplexer. A multiplexer and de-multiplexer may,in principle, be combined in a single device. Embodiments of the deviceare thus suitable for multicast applications.

An LCOS spatial light modulator in general has sufficient pixels for aplurality of kinoforms to be displayed upon a single device or die.Potentially hundreds of kinoforms may be displayed on a single LCOSdevice. Thus, in embodiments, the device may be configured to implementa set of beam routing functions using separate kinoforms displayed on asingle LCOS device, for example to provide a set of beamrouting/switching devices with shared optical components, for compactphysical implementation.

In some preferred embodiments the device includes a Fourier transferlens between the kinoform and replay plane; this may be corrected forchromatic aberration. In embodiments the LCOS SLM is a reflective SLM,the optical input(s) and output(s) are in substantially the same plane,and the Fourier transform lens is between the SLM and the input/outputplane.

In some embodiments of the device the calculation of the kinoform isoptimised for a particular wavelength, for example around 1.5 microns,but in other embodiments the calculation of the kinoform may beoptimised over a band of wavelengths, for example the optimal C-band(1530-1565 nm) and/or L-band, (1565-1625 nm). This latter approach isadvantageous as the device can then be fabricated to be substantiallywavelength agnostic, at least over a band of optical wavelengths, forexample of at least 10, 20, 30, 50 or 100 nm.

In embodiments of the device, and method described below, the targetreplay field may be chosen to perform a soft switch of the output beamfrom one position to another. This may be achieved by, when changing theselected optical output, defining a desired or target replay field whichtransitions from a current replay field or optical output to the desiredor target replay field or optical output via one or more transitionalstages or replay fields in which the currently selected output isattenuated and/or in which the new selected output is at an intermediateamplitude between zero and its desired (full output) level. Inembodiments a sequence of target replay fields may be employed toprovide a smooth transition from one optical output to another, forexample by fading one output down and another up. With such an approachit is particularly helpful to inherit a phase distribution for akinoform for a current replay field to use as the initial phaseddistribution for the kinoform for the next replay field in the sequence.Embodiments of the kinoform calculation procedure enable the use of thehologram of frame n as initialization for the calculation of frame n+1,discussed further in Bernau, M. “Improved hologram calculation forcorrelated video frames” International Conference on ConsumerElectronics (ICCE), Digest of Technical Papers, pp. 507-508, 2010.Moreover, the inheritance of a parameter used in the hologramcalculation from one frame to another can be successfully employed, forexample one or more feedback and/or gain parameters. Because the replayfields are relatively similar, this significantly speeds up theprocedure. Furthermore, embodiments of this approach provide animportant advantage in addressing problems with the dynamic response ofa liquid crystal material: it is undesirable when switching from onereplay field to another for, for example, the output replay field toeffectively flash with noise. By providing a gradual transition, such“noise flashes” can be substantially inhibited.

In a related aspect the invention provides a method of opticaltelecommunications light beam routing, the method comprising: displayinga kinoform on an LCOS SLM; providing an input light beam to said LCOSSLM; and diffracting said light beam with said kinoform to provide adiffracted output beam from said LCOS SLM; the method furthercomprising: calculating said kinoform displayed on said SLM using aping-pong algorithm.

In preferred embodiments the ping-pong algorithm comprises initialisinga phase distribution for the kinoform, for example randomly or based onan initial target replay field, calculating a replay field of thekinoform, modifying an amplitude distribution of the replay field butretaining the phase distribution, converting this modified replay fieldto an updated kinoform and then repeating the calculating and modifyingto converge on a desired target replay field. Preferably prior tocalculating the replay field the kinoform is modified using a model ofthe LCOS SLM response, in particular to take account of the limiteddeformation of the liquid crystal material which limits the phaseresponse of the pixels of the SLM, more particularly inhibiting largechanges in phase over a short distance (in pixels) across the SLM.

In preferred embodiments the kinoform is also modified to redistributethe amplitude noise away from a desired position of the output beam in areplay field of the kinoform, for example by increasing the size of thefield. In embodiments the procedure may also include a degree of overcompensation in the target amplitude replay field, for more rapidconvergence of the algorithm.

BRIEF DESCRIPTION OF THE DRAWINGS

These and other aspects of the invention will now be further described,by way of example only, with reference to the accompanying figures, inwhich:

FIGS. 1a, 1b and 1c show, respectively, an embodiment of an LCOS lightbeam routing device according to an embodiment of the invention, akinoform calculation procedure which may be employed in the device, andan embodiment of an LCOS light beam routing device incorporatingpolarization diversity.

FIGS. 2a and 2b show the position of a holographic switch in an opticalnetwork, and the optical arrangement of a holographic interconnect.

FIG. 3. A suggested arrangement of the input and output fibres (hereS_(max)=192).

FIG. 4. A telecentric f-theta lens will focus the beam at normal angleto the focal plane, its position will be proportional to the input fieldangle and the focal plane is flat.

FIG. 5. The apodisation losses as a function of the beam diameter.

FIG. 6. The dimensions of an LCOS device designed for holographicoptical interconnects.

FIG. 7. Hologram diffraction efficiency versus number of output users.Efficiency increases thus making holographic interconnects best suitedfor networks with many users.

FIG. 8. The sinc envelope formed at the output plane due to the squarepixel shape. Keeping fibres near the centre reduces attenuation.

FIG. 9. The two-dimensional sinc envelope attenuation as a contour map.

FIG. 10. The acceptable loss due to the sinc envelope as a function ofuseful area fraction. The two stars correspond to the proposed points ofoperation for the LOIS device.

FIG. 11. The diffraction efficiency of a phase quantised hologram. Fromthe top, efficiency for a single spot, a 100 and a 10 spot generatinghologram.

FIG. 12. The diffraction efficiency of a blazed grating with and withoutfringing fields for a device with the characteristics of LOIS.

FIG. 13 shows The diffraction efficiency of a blazed grating with andwithout fringing fields for a device with the characteristics of LOIS.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

Broadly speaking we will describe methods used to compute the pixelpatterns to minimise specific problems with using LCOS devices asdiffractive optical components in c-band to achieve telecoms standards,more particularly the control of signal beams in the telecommunicationsc-band by pixilated kinoforms on LCOS devices.

In embodiments the techniques concern the formation, splitting andconditioning of optical signal beams in the telecommunications 1.5micron wavelength window by means of computer generated hologramscomprising patterns of programmable phase-modulating pixels dynamicallydisplayed on suitably designed liquid crystal over silicon (LCOS)devices. In particular, we are primarily concerned with using parallelaligned nematic LCOS devices which provide a phase-only modulation ofthe reflected light beam with insignificant amplitude modulation.Contemporary versions of such devices have been described in N Collings,T Davey, J Christmas, D Chu, and B Crossland, “The applications andtechnology of phase-only liquid crystal on silicon devices” (InvitedReview), IEEE/OSA J Display Techn Volume: 7, Issue: 1, Date: 2011,Pages: 112-119. These devices do not convert the polarisation of theincident light into the orthogonal polarisation in reflection(polarisation crossover).

In particular the techniques concern the improvement in quality of thesebeams such that they may be efficiently directed into single mode outputfibres in a manner that ensures high beam quality and minimum crosstalkof the signal carried in the output fibres, thereby meeting therequirements of telecommunication systems.

To achieve this we use specific techniques to compute the pixel patternsof pixilated kinoforms to be displayed on the LCOS devices used todiffract the signal beams, in particular to resolve the specificproblems that arise in reconfigurable dynamic diffractive devices madepossible by LCOS technology and operating in the near-infra-red. Theseapplications present special problems as previously outlined in theintroduction.

Simple pixel patterns that consist only of periodic gratings displayedon practical LCOS devices do not meet the requirements for efficiency,low noise and crosstalk. We describe pixel patterns which arenon-periodic and are generally derived with the aid of iterativecomputer algorithms, optionally using tailored cost functions, toproduce telecommunications devices operating in the near infra-red. Thecost functions can be written so that the loss of light intonon-selected output fibres (crosstalk) carries a high cost and theresulting hologram will exhibit the very low levels of crosstalkrequired for a commercial system.

The techniques we describe facilitate: Multicasting, for example makingpossible multiple functions carried out by one device; the opening up ofthe full 2D interconnection plane; crosstalk minimisation; aberrationcorrection; and adding new functions to the diffractive structure (e.g.channel equalisation).

In broad terms, the iterative methods used to derive the pixel patternsdo not assume periodicity. Thus they intrinsically minimise thelimitations caused by fitting periodic pixel patterns into finite pixelarrays. These methods implicitly assume that each pixel has its owndiscrete phase retardation, i.e. the phase profile is assumed to bequantised and they intrinsically minimise the quantisation noiseresulting from the pixel structure. They can recognise that extent ofthe pixel pattern is finite by allowing optimisation is carried out onthe convolution of the pixel pattern with the aperture function of theholograms. An aperture function can be incorporated into the kinoformgeneration routine to achieve an output amplitude profile designed tomaximise the coupling of the beam into the output fibre.

To increase the computation speed, but also to minimise crosstalk andnoise, the algorithms may be modified with over compensation and don'tcare regions. The iterative algorithms may be designed to adaptivelyadjust the pixel pattern of the pixilated kinoform to accuratelyposition the output beam and the maximise the overlap integral with theoutput fibre.

Embodiments of these methods also recognise that liquid crystal phasemodulators cannot reproduce very high spatial frequencies. The pixelpatterns may be optimised under this assumption to minimise lightdissipated by deflection into symmetric orders. Further, the pixelpattern may be modified by adding to it an overall phase function tobring signal light to a focus in a different plane compared to eithernoise resulting from the quantisation of the hologram pattern orresidual light in the zero order. This increases the signal to noise ofthe signal beams, in the latter case allowing the spatial filtering ofthe zero order light. The pixel pattern may also be modified by addingto it an overall phase function to correct for aberrations orinaccuracies in the optical module.

Still further the methods allow some modification of the wavelengthselectivity of the diffracting pattern to achieved, allowing pixilatedkinoforms to be designed that show minimum ‘roll-off’ with wavelengththroughout c-band, permitting wavelength agnostic switching within thisband.

In embodiments the invention relates to methods to realise an acceptableperformance and functionality for programmable pixilated kinoformshaving a phase excursion equal to or greater than 2π (to enable a 2πrange of phase modulation). The pixel patterns are displayed on a LiquidCrystal over Silicon (LCOS) micro-display within a telecommunicationsmodule to carry out optical signal processing. The pixel patterns arecomputed using iterative algorithms and do not consist of periodicgratings but of non-periodic building blocks. They diffract nearinfra-red light, whose wavelength lies in a communications band, tochosen output locations.

In embodiments of the methods we use algorithms for computing thekinoform pixel patterns in real time that are based on the Fast FourierTransform algorithm applied to the entire kinoform pixel block. Theyembody over-compensation and ‘don't care regions’ to increase efficiencyand minimise noise. The kinoform pixel patterns are calculated to takeaccount of the limited deformation that can be suffered by the nematicdirector of the liquid crystal when an electric field is applied. Thekinoform patterns may be modified to allow beam splitting and beamattenuation. The kinoform pixel patterns may also be modified tominimise the wavelength selectivity over the telecommunication band inuse. In embodiments we add optical additional optical components modulo2π to the phase profile of the main kinoform. We are able to deflectbeams in/out of spots and spot arrays.

In embodiments the kinoform is generated in a processor and programmedfor representation by the LCOS; it comprises a representation of a phasehologram. As this technique relies on phase only modulation there is nolight loss through amplitude modulation. We use a class of algorithmwhich can compute the kinoform in real time, preferably employing hardwired fast Fourier transform processor(s). The procedure is based on aclass of bi-directional iterative optimisation algorithms referred to asping-pong algorithms (for example IFTA, Gerchberg Saxton). We optimise arandom or deterministic phase distribution in the phase (kinoform) planeby mapping it to a second plane where there are known constraints. Thedistribution is then re-mapped to the phase plane, the amplitude isconstrained to unity, and the process is repeated until a satisfactoryphase distribution in the phase plane is achieved.

In embodiments we adapt this procedure to employ a method forapproximating the one and two dimensional phase profile on an LCOSdevice to compensate for finite liquid crystal deformation, and use thismethod to compute the optimum voltage profile on the LCOS electrodes sothat the system performance (for example crosstalk and/or stability ofthe system with changing environmental conditions) is optimised. Forexample to estimate the liquid crystal profile we can employ a “springmodel”, in effect a low pass filter (equivalent to convolution with akernel). The filter's parameters (or convolution kernel) may becalculated using only a pair (in 1D) or four (in 2D) neighbouringpixels. (The behaviour of these two (or four) pixels under variousvoltages may be simulated using computationally demanding techniquesthat solve the complex continuum equations, for example Finite ElementMethods or Tensor Methods). In embodiments we include such a low-pass(spatial) filter or convolution in the iterative loop for computing thekinoform so that the resulting kinoform is tolerant to a high degree ofthe LC imperfections and in particular to the inability of the LC tobend significantly.

EXAMPLE IMPLEMENTATION

Referring to FIG. 1a , this shows an embodiment of an LCOS light beamrouting device 100 according to an embodiment of the invention. A fibreoptic array 102 comprises one or more input fibre optics 102 a and aplurality of output fibre optics 102 b, with inputs and outputs in acommon plane 104 (the kinoform replay plane). An LCOS SLM 106 displays aphase pattern of a kinoform and operates in a reflective mode. AFourier-transform lens 108 is located between the replay plane 104 andkinoform/SLM 106. The SLM is driven by a data processor 108 which has aninput 110 to receive routing data for selecting an optical output. Thedata processor in embodiments performs the calculations as describedbelow to determine an output kinoform data for SLM 106. In embodimentsone or more of the input and/or output beams may be monitored by a beammonitor 112, for example a detector array. The skilled person willappreciate that there are many monitoring techniques which may beemployed including, for example, splitting off one fibre optic fromanother. Additionally or alternatively a separate output port may beprovided for monitoring purposes. An output from monitor 112 is providedto data processor 108 for optional use in an initial calibration so thata target replay field function can be adjusted to optimize, moreparticularly maximize coupling such as an overlay integral between thedeflected light beam and the input of a fibre optic.

The data processor 108 implements a kinoform calculation procedure ineither software, hardware, or a combination of the two. It isparticularly preferred to perform a Fourier transform procedure of thecalculation in hardware, for speed/efficiency.

Referring to FIG. 1b , this shows an embodiment of a kinoformcalculation procedure which may be employed in data processor 108,according to an embodiment of the invention.

Thus at step 150 phased data for the kinoform is initialised, forexample for a grating-type solution in one or two dimensions, sincebroadly speaking this should correspond to deflection of an input beamto a desired output position. Optionally this initialization may includesuperimposing a lens on the phase pattern to focus the output beam ontothe input of an output fibre optic; a Fourier transform may be employedto implement this. In general this initialization will assume unityamplitude for the output beam, although optionally a different amplitudemay be employed, for example to implement channel equalization. Althoughinitializing the phase pattern to a grating-like solution is convenient,this is not essential and in other approaches, for example, a randominitialization may be employed.

At step 152 the phase pattern is modified to take account of the liquidcrystal response of the LCOS SLM. In embodiments this may be performedby a digital filter (low pass filter) or convolution step, as describedin more detail in Georgiou et al (ibid).

Then, at step 154, the data processor 108 calculates a replay field ofthe kinoform, which comprises a phased component and an amplitudecomponent. The phase component is retained and, in embodiments, theamplitude component is replaced by a desired replay field such asillustrated example 120. For noise reduction this may be expanded 130beyond a perimeter 122 of the fibre optic outputs.

The step 156 of replacing the calculated amplitude component of thereplay field with a desired target replay field preferably also includesa check on whether the difference between the calculated and desiredamplitude is less than a threshold level, in which case the procedurehas completed and outputs 158 the kinoform data. The skilled person willappreciate that any of a range of different measures may be employed asto whether or not the difference between the calculated and targetamplitude components of the replay fields are within a tolerable bound.

If the procedure does not complete then, at step 160, the previous phasecomponent and new amplitude component of the replay field becomes thenew target replay field and a space-frequency transform 162, inparticular a Fourier transform is performed to convert this to thekinoform plane. The procedure then loops back to step 152, to againmodify this new phase pattern by low-pass spatial filtering, to againincorporate the effects of the liquid crystal response. The procedurethen continues around a loop, interacting until the desired kinoformdata is output.

Referring now to FIG. 1c , this shows and an embodiment of an LCOS lightbeam routing device 180 incorporating polarization diversity. Likeelements to those of FIG. 1a are indicated by like reference numerals.In this embodiment a polarizing beam splitter 182 splits the twopolarizations of the light into s-polarization incident on SLM1 106 a(dotted line) and p-polarization incident on SLM2 106 b (solid line).The two polarizations are separately diffracted and brought togetheragain on the output fibre. The alignment of the liquid crystals in thetwo SLMs is appropriate to the incident polarization.

Further Considerations when Multicasting Optical Interconnects UsingLCOS Devices

We now describe the characteristics and expected capabilities of anoptical interconnect that uses a diffractive Liquid Crystal over Silicon(LCOS) device as routing element. Such an interconnect may be used in aneighbourhood's optical network to distribute high definition televisionthus avoiding an electronic or optical transmitter for each user. Theoptimal characteristics of the LCOS device are calculated in terms ofpixel number and silicon area and found to be feasible with today'stechnology. Finally its performance in terms of optical efficiency andnumber of output ports is evaluated and found suitable for aneighbourhood with 100's of households.

Future optical networks will rely more on optical interconnects. Theycould be used to restore a network after a link failure, dynamicallydistribute bandwidth and remotely connect or disconnect users. Whenfibers to the home (FTTH) are more widely installed opticalinterconnects will provide a flexible and low cost method for adding orremoving high bandwidth users into the network; for example in videosignal distribution where a large number of outputs and multicasting isrequired.

The download rate of any home user will be significantly larger than theupload rate. Therefore the strain in the network will be from theservice provider to the user. A television viewer may easily besubscribed to a couple of hundred channels of which he/she wants instantaccess. If these channels are in 1080p, possibly some with 3Dfunctionality, the bandwidth requirements are significant. In addition,if some users request video on demand, the total number of videochannels being delivered in a neighbourhood from the service providercould reach a thousand. Personalized content will be encrypted (similarto a wireless network). With a thousand channels at high definition, thetotal bandwidth requirement is of the order of Gbps. At this bitrate,the conversion from optical to electrical signal is expensive and ismade at the user. Routing the signal in the optical domain eliminatesthe need for an optical-electrical-optical conversion at the exchangeand a high-speed electronic router.

FIG. 2a shows how the switch could be used in a HDTV distributionnetwork. By generating a high-power optical signal and then distributingusing an optical interconnect the use of an electronic or opticaltransmitter for each user is avoided reducing hardware and installationcosts. In the future, a single powerful laser (of which its polarizationis carefully controlled) could provide power to 10's or 100's of usersand distributed by an optical interconnect.

Note that liquid crystal materials due to their rod-shaped molecularstructure will affect each polarization of the laser in a different way.This is not an issue when the laser source is physically next to theLCOS device and its polarization is set parallel to the liquid crystalmolecules. In this case, the polarization effects are controlled and thephase excursion of the incident wave is maximized. Some smallpolarization modulation may be observed between pixels of differentvoltage but their effect will be significantly smaller of the fly backeffects (discussed later).

The advantage of holographic interconnects over competing technologiesis their ability to only route power to the selected ports. Thusefficiency is not affected by the number of potential users, S_(max),but by the number of connected users, S. In a holographic switch thepower per output channel is given by ηP_(in)/S (see FIG. 2a ) where η isthe power efficiency of the interconnect and P_(in) the power input intothe switch. This makes holographic switches ideal when the number ofpotential users, S_(max) is large but at any moment only a fraction ofthose are connected, like the distribution of video in a neighbourhood.Service providers like to have all households as potential customers,S_(max), but at any moment only a number, S, of them is connected.

Other technologies, can multicast but they base their operation inblocking light from the non-connected users. This brings the power peruser down to ηP_(in)/S_(max) compared to ηP_(in)/S for a holographicswitch. Thus a holographic switch gives the flexibility to have a largenumber of potential users, S_(max), while not losing any power for thisflexibility.

Another advantage of a holographic interconnect it its ability toperform additional functions for the network. The hologram can re-writethe phase profile of the beam and thus correcting for defocus,astigmatism or misalignment, thus improving the power coupling into theoutput fibres. Other functions include channel equalisation, noisesuppression and the provision of monitoring channels.

This present an optical arrangement for a system together with theory onholographic switching; the sources of loss in a holographic interconnectand gives a theoretical estimate of the system efficiency; an estimateto the number of output ports possible in a holographic switch; and anoverall presentation of the system, suggesting characteristics of theLCOS device.

Holographic Interconnects

Holographic optical interconnects use diffraction to route light to thetarget output fibres. FIG. 2b shows an optical arrangement used inholographic interconnects. The beam emerging from the input fibre, witha Gaussian-like profile, expands and then it is collimated by a positivelens. The LCOS device, with dimensions L×L, modulates the phase of theincident beam, introducing high frequency components. The reflected beamis focussed by the lens that in effect Fourier transforms the beamprofile. This makes the beam focus to move on a different position orpositions depending on the phase pattern on the device.

The illumination profile on the device can be approximated by a Gaussianprofile. Its width is given by the Fourier transform of the near fieldthat is also a Gaussian. The two beam widths are related by:

$\begin{matrix}{{2w_{d}} = {\frac{4\lambda}{\pi}\frac{f}{2w_{i}}}} & (1)\end{matrix}$

where f is the focal distance of the lens, λ the optical wavelength,2w_(d) the beam width on the LCOS device and 2w_(i) the beam width ofthe input source (see FIG. 2). In a Gaussian profile, the beam width isdefined as the circle diameter where intensity drops to 1/e² of its peakvalue.

The size of the output beam is also given by Eq. 1. If the beam is notheavily apodised, which is the case to minimise optical losses, 2w_(o),the output beam width is equal to 2w_(i) the input beam width. If theinput fibre has the same diameter as the output fibres the output beamwould fit exactly into the output fibre. Increasing the diameter of theoutput fibre relaxes the tight constrains on spot size and positioningand coupling efficiency will improve. This could be done by the use of amulti-mode fibre (MMF), a taper fibre or a micro-lens. The opticalfibres are expected to operate at 1.3 μm, 1.5 μm or 850 nm and bearranged in a rectangular grid as shown in FIG. 3. The input fibre willbe placed in the centre of the grid. The LCOS device may have a smalltilt in relation to the input fibre to eliminate any unwantedreflections entering back into the input fibre. As the cladding ofsingle mode fibre (SMF) has a 125 μm diameter, the spacing betweenoutput fibre cores is also at least 125 μm.

Efficiency

The optical efficiency of an interconnect is defined as the power of theoutput signal over the input signal. Each user should receive a certainminimum power. Given that input power, P_(in) may not be controlled bythe interconnect, efficiency η, determines the maximum number ofconnected users. Thus high efficiency will allow more users to beconnected.

Values of acceptable efficiency vary widely and depend on theapplication and other functions of the system. MEMS cross connects withefficiencies better than −7 dB have been reported with up to 256 inputsand outputs. However, the particular system has a different role in thenetwork as it may not multicast or broadcast. Because holographicswitches can dynamically control the power of each output channel,outputs connected with lossy links may be boosted to achieve fairerpower distribution and this will allow more users to be connected.

Efficiency strongly depends on the choice of the appropriate LCOSdevice. Most commercial LCOS devices are designed for displayapplications where pixel count is maximised and device area isminimised. Some LCOS devices have been designed specifically forinfrared operation, like the Roses. In this work four custom devices areproposed and their performance is evaluated. The first device, refereedto as the LCOS for Optical Infrared Switching (LOIS), is larger in termsof active area and has fewer pixels compared to most commercial devices.Scaled down versions of LOIS, the mLOIS, μLOIS and nLOIS are alsoconsidered. In addition a number of commercial devices are presented andare shown together with the proposed ones in the Table below.

Device Name Δ/μm g/μm N F L/mm Area/mm² Dimensions Manufacturer LOIS18.0 0.25 1024 0.97 18.4 339 18.4 × 18.4 — mLOIS 18.0 0.25 720 0.97 13.1169 13.2 × 13.2 — μLOIS 18.0 0.25 512 0.97 9.2 85 9.1 × 9.1 — nLOIS 18.00.25 164 0.97 2.9 8.7 2.9 × 2.9 — 4K2K D-ILA 6.8 0.25 2400 0.93 16.3 36416.3 × 26.1 JVC BR1920HC 9.5 0.40 1200 0.92 11.4 208 11.4 × 18.2Brillian JVC 9.5 0.45 1080 0.91 10.3 187 10.3 × 18.2 JVC ProfessionalQualia 9.0 0.35 1080 0.92 9.7 168  9.7 × 17.3 Sony JVC 8.1 0.45 10800.89 8.7 136  8.7 × 15.6 JVC Consumer 7.0 0.35 1080 0.90 7.6 102  7.6 ×13.4 Sony Sony XBR

The optical loss, not directly linked with the holographic nature of theinterconnect is not considered here. These include back reflections,mirror reflectivity and coupling losses. Note that the efficiency of theswitch could be significantly affected if the optical system and thefibre array are not designed appropriately.

Thought the hologram can deflect the beam by a range of angles theFourier lens should be diffraction limited for all the range. Inaddition, the launch angle into the output fibres should be normal tomaximize insertion efficiency. Aspheric lenses with thesecharacteristics include telecentric F-theta lenses. They can ensure thatthe beam incidents on the output fiber array at normal angle(telecentric operation) and that the position of the focus isproportional to the field angle (F-theta operation). In addition, thefocal plane is flat instead of curved. This is shown graphically in FIG.4. An alternative way to eliminate the issue of the oblige incidence isto use a second hologram that deflects the beam in the oppositedirection by the same amount. This arrangement, router-selectorarchitecture, is used to transform the switch into a crossbar switch.

Another challenge is the construction of the densely packed array shownin FIG. 3. Such an array is feasible but it is likely to be anengineering challenge. Nevertheless, waveguide technology has beenconstantly improving. Waveguides with fifty thousand fibers arecommercially available (e.g. Sumitomo Image Guide IGN-20/50) and usedfor optical fiber image guides with core spacing of less than 10 μm.Fibers, and especially fiber arrays, will have their core slightlymisplaced and if this is not considered, efficiency will be furtherreduced. There are a few ways to minimize and even eliminate the issue.The hologram can use heuristic techniques to identify the exact centreof the fiber and then reconfigure for the revised positions. This shouldinclude some kind of feedback from the fiber. Another way to addressthis issue is to increase the diameter of the SMF using a taper fiber ora micro-lens. This technique has the advantage that the effectivediameter of the core increases while the fiber remains single mode.

Finally, a MMF may be used though it may not always be desirable to useboth SMFs and MMFs in the same network. Nevertheless, for shortdistances the MMF may be the most cost effective solution in terms ofhardware.

The losses considered here are associated with the (i) device fillfactor (ii) beam apodisation (iii) hologram efficiency and (iv)phase-rendering. In the following four subsections these losses areconsidered in detail.

Apodisation

Apodisation losses refer to the trimming of the Gaussian profile by theLCOS device. The amount of apodisation is determined by the focaldistance of the lens: a large focal distance will create a broadGaussian function with large trimming of the profile. There is atrade-off in choosing the optimal focal distance. It is desirable tominimise losses by having small f and concentrating more power on thedevice. At the same time it is also desirable to use all the availablepixels because this increases the number of output ports. Given theimportance in optical efficiency it may be appropriate to use moresilicon area rather than increase loss. Apodisation also changes thesize and the shape of the focal points reducing power coupling into theoutput fibres. Limited beam shaping is possible by using the LCOSdevice. The amount of energy landing on the active area of the device,P_(d) is given by:

$\begin{matrix}{P_{d} = {\frac{1}{w_{d}\sqrt{2\pi}}{\int_{{- L}/2}^{x = {{+ L}/2}}{\int_{{- L}/2}^{y = {{+ L}/2}}{e^{{{- {({x^{2} + y^{2}})}}/2}w_{d}^{2}}{dxdy}}}}}} & (2)\end{matrix}$

where w_(d) is a function of focal distance, f. The apodisation loss fordifferent focal distances was calculated by integrating the power overthe square area of the device using the above integral. FIG. 5 showsthis variation with the horizontal axis showing the beam size incomparison to the device size and the vertical axis the optical loss. Itcan be seen that for a beam width of about 0.4L the apodisation is verysmall and less than −0.1 dB. Above this, apodisation loss issignificant. Thus it is recommended that the beam width is about 0.4L.

Fill Factor

LCOS devices are silicon devices in which a layer of reflective metal,like aluminium, is deposited on top of the silicon backplane. Pixels actboth as mirrors and electrodes thus they should be separated by anon-conductive area, refereed to as inter-pixel gap or dead-space. Incommercial devices, this space can be as low as 0.25 μm. Note thatdevices with dielectric mirrors may have zero inter-pixel gap but theassociated fringing fields are significant. Inter-pixel gap reduces theaverage reflectivity of the device by a factor F, the fill factor, whichis equal to

$\begin{matrix}{F = \left( \frac{\Delta - g}{\Delta} \right)^{2}} & (3)\end{matrix}$

where Δ is the pixel pitch in the x and y direction on the device planeand g is the inter-pixel gap as shown in FIG. 6. Both inter-pixel gapand pixel pitch are the same in both directions.

For a rectangular device with active area L×L and N×N pixels the fillfactor can also be expressed as

$\begin{matrix}{F = \left( {1 - {\frac{g}{L}N}} \right)^{2}} & (4)\end{matrix}$

In this equation, the inter-pixel, g, is fixed by the lithographicprocess. The dimensions of the active area, L, heavily affects the costof the device and thus it is also constrained. Only the number ofpixels, N, may be treated as a free variable when optimising the system.Increasing the number of pixels for a fixed silicon area will increasethe number of the output fibres (smaller pixels thus larger deflectionangle) but will also increase the fill factor losses. Thus for a givennumber of outputs, the minimum number of pixels should be used.

Despite the large cost of silicon per mm² an interconnect will have ahigher value and longer lifetime than a consumer appliance allowinglarger silicon devices. Increasing the size improves fill factor and theoverall efficiency of the system. It is proposed that LOIS has only 1024pixels but an active area of 18.4×18.4 mm thus having a fill factor lossof only 0.15 dB.

Hologram Efficiency

Hologram efficiency here refers to the theoretical maximum energy aphase-only hologram can deliver to the target positions. The hologramcan modulate only the phase of the incident beam and not its amplitude.This introduces ghost orders that reduce the diffraction efficiency.Depending on the arrangement of the output ports the diffractionefficiency of the hologram may vary from 0 dB (for a blazed grating) toabout −1 dB (see FIG. 7).

There is not an analytical way to calculate the exact hologramdiffraction efficiency for any arbitrary port arrangement. However, theworst case scenario is for two output ports when the diffraction losscan be analytically calculated and it is equal to 2 sinc(π/2) or −0.9 dB(this is found in the same way as the efficiency of a binary-phasehologram, see above). Increasing the number of multicasting outputs,reduces the power per output fibre, ηP_(in)/S but improves the overallefficiency, η. The best case scenario is when there is only one output,in which case the diffraction efficiency is unity.

In order to estimate the ideal diffraction efficiency of the system, anumber of holograms were computed using the Output Plane PhaseOptimisation (OPPO) method and Direct Binary Search (DBS). The number ofselected output ports, S, was varied from 1 to 192. For each S, 40different combinations of output fibres were made and for eachcombination a hologram was designed to route light to them. The outputfibres were placed on a regular grid of 15×15 with the central fibre ofthe grid being the input as shown in FIG. 3. Eight fibres on each cornerwere not used in order to form a more circular arrangement. Thus thetotal number of output fibres was 192. The solid line in FIG. 7 showsthe mean diffraction efficiency for any number of spots from 1 to 192.The dots show diffraction efficiencies of individual holograms. It canbe seen that the optical loss is always better than −1 dB and improvesas the number of output channels increases. The grey line shows theenergy per user. The power per user is not constant but increases as thenumber of user decreases thus making better utilisation of the availablepower.

Note that if necessary the hologram design can reduce the crosstalk ofthe interconnect down to acceptable levels. This can be done in a numberof ways. First, all predictable imperfections of the system may beincluded in the hologram design algorithm and their effect eliminated.These include phase quantization, pixilation, inter-pixel gap and eventhe fringing fields between neighboring pixels. Non-predictable errors,like device flatness, thermal drifts and misalignments can be minimisedby adding the appropriate Zernike coefficients on the LCOS device. Manyauthors have investigated ways to calculate in real-time these errorsand compensate for them. Finally, the great strength of holograms liesin the fact that most device imperfections will be transformed into theFourier domain thus they are likely to arrive either on the zero orderor as high frequency component noise. Currently one-to-one opticalswitches are used as commercial systems and their performance in termsof crosstalk is acceptable.

Phase Rendering Losses

Real LCOS devices do not render the phase profile perfectly thusadditional optical losses are introduced. There are three main sourcesof phase errors in a device: spatial quantisation or pixelation, phasequantisation and electric field fringing.

Spatial Quantisation

Square pixels on an LCOS device act as apertures forming a far field onthe output plane. All pixels have the same shape but are shifted inspace. Space shifting on the hologram plane translates to phase shiftingin the output plane. Therefore on the output plane the far field of eachpixel will have the same amplitude and position but different phase.Adding the effect of all pixels together, it will form a far fieldamplitude envelope with the same shape as the far field of a singlepixel. The far field of a square pixel is a two-dimensional sincfunction and it is given by:

η_(sinc) =F sinc²(uK)sinc²(vK)  (5)

where K is given by:

$\begin{matrix}{K = \frac{\pi \; \Delta}{\Delta - g}} & (6)\end{matrix}$

and u and v are the normalised horizontal and vertical coordinates onthe output plane. The normalised coordinates of the output plane areunity at position if or at deflection angle

$\frac{\lambda}{\Delta}.$

FIG. 8 shows the sinc envelope in one dimension when the fill factor isunity (solid line). The thick gray line shows the range of attenuationwith the commercial devices shown in the Table above, and the dottedline for the four LOIS devices. The horizontal line shows the normaliseddeflection angle. The maximum normalised deflection angle in aholographic interconnect is ±0.5 when the period is two pixels. Abovethat spatial frequency, aliasing occurs.

In two dimensions the sinc envelope will form a top hat function. Thenearer to the center a beam is deflected, the less the attenuation.Since the area available on the output plane is limited, the more portsare placed the more attenuation should be sustained by the ports furtheraway form the zero order. This is shown on a two-dimensional contour mapin FIG. 9. It corresponds to the ideal case when fill factor is unity.It shows that if a maximum −0.5 dB loss is acceptable due to the sincenvelope, only the area of the central contour may be used. Thiscorresponds to a fraction of 0.15 of the total output plane area. Theratio of the area where output ports may be placed over the total areawill be denoted by the parameter α. If higher loss is acceptable, α islarger. For an acceptable loss of −3 dB, α is about 0.6 and thisincreases the area of the useful output plane and the number of theoutput ports. Loss for real devices will be lower due to reduced fillfactor. The amount of available area for a given efficiency reductiondue to the sinc envelope is given in FIG. 10.

Phase Quantisation

Phase quantisation is caused by the limited palette of voltages thesilicon backplane can provide. In general, a digital-to-analogueconverter (DAC) will provide the analogue voltage driving the liquidcrystal cell. More phase levels will increase the complexity of the DACand could reduce its speed. Therefore, it is important to design a chipwith the least possible number of phase levels.

For a general multicasting hologram the efficiency reduction due tophase quantisation cannot be calculated analytically. However, theefficiency η_(pq) of a phase-quantised blazed grating can be calculatedand it is equal to:

$\begin{matrix}{\eta_{pq} = {\left\lbrack {\int_{{- \pi}/p}^{\theta = {\pi/p}}{{\cos (\theta)}d\; \theta}} \right\rbrack/\left\lbrack {\int_{{- \pi}/p}^{\theta = {\pi/p}}{1d\; \theta}} \right\rbrack}} & (7) \\{= {\sin \; {c\left( \frac{\pi}{p} \right)}}} & (8)\end{matrix}$

where p is the number of available phase levels and θ corresponds to thephase delay introduced by a pixel relative to the phase of the targetspot. The first square parenthesis gives the intensity of the beam whenthere were only p phase levels and the second square parenthesis whenthere are infinite phase levels. Efficiency is the ratio of the two.

The effect of phase quantisation for holograms with more than one outputwas estimated by computing holograms with different quantisation levelsand then comparing their performance. This is shown in FIG. 11 forholograms with one, 10 and 100 output ports. Each efficiency point wascalculated from 15 different holograms with 1024×1024 pixels. Loss dueto phase quantisation is negligible above 32 phase levels. It istherefore suggested to use at most 32 phase levels or 5-bits per pixel.

Fringing Fields and Liquid Crystal Deformation

The phase modulation in an LCOS device occurs in the liquid crystalmaterial that is being rotated to the desired orientation by theelectric field. FIG. 3 shows a cross section of the liquid crystal layeron an LCOS device. As the thickness of the liquid crystal cell increasesthe electric field between the pixels increases compared to the fieldbetween the pixel and the top electrode. This creates a smoothing effectfor the phase profile that is affecting large phase transitions on thehologram, especially the 2π phase jumps of a blazed grating. This 2πphase jump is usually referred to as flyback.

Calculating the liquid crystal behaviour on a large hologram with abouta million pixels is computationally difficult. It requires the solutionof the continuum theory equations for the entire device. There are a fewcomputationally efficient approximations to estimate the behaviour ofthe liquid crystal. In this paper we use the low-pass filter approach,in which the phase profile is estimated by convolving the ideal profilewith a kernel. The shape and width of the kernel is found by solving thecontinuum theory equations for two neighbouring pixels using a FiniteElement Method (FEM) software.

The effect of electric fringing field, and thus the width of the kernel,increases as the thickness of the cell. So it is important to have asthin cell as possible but that achieves 2π phase modulation. In practiselarger phase excursion is used to reduce the maximum rotation angle ofthe liquid crystal and increase speed. The thickness of the cell for a φmaximum phase excursion is given by:

$\begin{matrix}{d = {\frac{1}{2}\frac{\phi}{2\pi}\frac{\lambda}{\Delta \; n}}} & (9)\end{matrix}$

where Δn is the birefringence of the liquid crystal. The term ½ arisesbecause the device operates in reflection thus the wave is modulated inthe way in and in the way out. For a 2.5π phase modulation, 1.55 μmwavelength and using E7 liquid crystal the cell thickness is 4.8 μm.Simulating this device using continuum theory in a FEM software givesthe kernel of the low pass filter.

Using this one-dimensional kernel, the efficiency of a blazed gratingwith all possible deflection angles was found and it is shown in FIG.12. Fringing fields affect the diffraction efficiency of the grating butthe difference between the ideal sinc envelope efficiency (dotted line)is small and never more than −0.5 dB. If both dimensions are considered,the maximum loss will be −1 dB. The maximum discrepancy between the twocurves occurs when the period is roughly four pixels, i.e. thenormalised deflection angle is 0.25.

Two factors make FIG. 12 to show the worst case scenario. First, in ablazed grating the entire area of all the pixels contribute to theoutput port, and thus efficiency is unity. Any discrepancy willcertainly create a profile with lower efficiency. For any otherhologram, each pixel contributes to many output ports and a discrepancyin its phase will have a smaller effect into the output (this wasverified by adding random noise to a blazed grating and a multicastinghologram and the effect on the latter was less). Second, part of thefringing fields occur on the pixel boundary, were some of the loss hasalready been accounted by the inter-pixel gap. As the size of theinter-pixel gap is smaller than the wavelength and the propagationdistance within the liquid crystal considerably more, the effect of theinter-pixel gap cannot be easily accounted for (it can be accounted bysolving the Maxwell equations within the anisotropic liquid crystal andthe metal electrodes).

Fringing fields do change the shape of the sinc envelope on the outputplane as it can be seen from FIG. 12. Consequently, so does thevariation of α as a function of loss.

This change, which is rather small, is accounted together with the sincenvelope in the Results and Discussion section below. FIG. 13 shows thediffraction efficiency of a blazed grating with and without fringingfields for a device with the characteristics of LOIS.

Output Ports

The number of selected output fibres in a holographic interconnect isrestricted by the diameter of the fibres and the accessible area on theoutput plane. The positioning of the output spots can be done with highaccuracy by the hologram but the point spread function (PSF) of thespot, i.e. size of the spot, should be the same size or smaller to thecore of the output fibres (d_(Fo)). The area occupied by the cladding ofthe output fibre, with diameter D_(Fo), takes useful space but no outputports can be placed there. Assuming a rectangular grid, each output portwill occupy D_(Fo)×D_(Fo) area on the output plane (see FIG. 3).

The area of the entire output plane is given by the maximum deflectionof the hologram which is

$\begin{matrix}{u_{\max} = {{{\pm \frac{\lambda \; f}{2\; \Delta}}\mspace{14mu} {or}\mspace{14mu} u_{\max}} = {{\pm 0.5}\left( {N\frac{\lambda \; f}{L}} \right)}}} & (10)\end{matrix}$

giving far field area of (Nλf/L)². However, the useful area of theoutput plane is less because parts of the far field are highlyattenuated by the sinc envelope. If only a fraction a of the far fieldarea is used, then efficiency is increased because the high-attenuationarea is not used. This gives a total number of output fibres, S_(max)equal to

$\begin{matrix}{S_{\max} = {\alpha \left( \frac{N\left( {\lambda \; f} \right)}{{LD}_{Fo}} \right)}^{2}} & (11)\end{matrix}$

The wavelength and the focal distance terms may be eliminated byconsidering that the size of the output spot, 2w_(o), should be smalleror equal to the output fibre core size, d_(Fo), such that

$\begin{matrix}{{2w_{o}} = \left. {{\frac{4\; \lambda}{\pi}\frac{f}{2w_{d}}} \leq d_{Fo}}\Rightarrow{{\lambda \; f} \leq {\frac{\pi}{4}2w_{d}d_{Fo}}} \right.} & (12)\end{matrix}$

giving the maximum number of output ports to be

$\begin{matrix}{S_{\max} = {{\alpha \left( \frac{\pi}{4} \right)}^{2}\left( \frac{d_{Fo}}{D_{Fo}} \right)^{2}\left( \frac{2w_{d}}{L} \right)^{2}N^{2}}} & (13)\end{matrix}$

The above equation contains five factors. The first factor, α, statethat the number of output ports, S_(max), can increase by reducing theefficiency of the system. The second factor,

$\frac{\pi}{4}$

is determined by the packing factor of the fibres and it is equal to theratio of the fibre's cross section area over the area of a circumscribedsquare (for hexagonal packing this ration will be

$\frac{\pi}{2\sqrt{3}},$

an increase of 15%). The third term is determined by the relative sizeof the core to the cladding. For a single mode fibre this is about

$\frac{10\mspace{14mu} \mu \; m}{125\mspace{14mu} \mu \; m}.$

The fourth term is determined by the apodisation. Assuming the optimumapodisation is used, it will be equal to 0.4. Finally, the last term N²,is the total number of pixels on the device.

It is interesting to note that the number of output ports is not afunction of the wavelength or the focal length. It can also be increasedby any amount by increasing the number of pixels but it should also beaccompanied by a suitable increase of the LCOS active area, L×L, to keepα and thus the losses constant.

Discussion

In the previous sections the parameters affecting the performance of aholographic interconnect were determined. In this section the system isconsidered as a whole and its characteristics are discussed withrelation to different applications.

Area

The active area of the device is possibly the most important parameterof the LCOS device as it directly affects number of pixels, number ofoutput ports and cost. The cost of a device is directly linked to itsarea with large devices being disproportionately expensive. As a guide,commercial silicon chips should be sufficiently small to keep thethroughput high. The Intel Xeon x7460 processor for example has 503 mm²die area and Intel Xeon x5405 has 214 mm² area. The JVC 4k LCOS devicehas active area of 546 mm². The proposed devices, have active area ofranging from 340 mm² to 9 mm². Even the top range LOIS device, with 340mm² area, it is within the limits of current fabrication techniques, interms of silicon area and cost. Note that the LCOS device in an opticalinterconnect would be only a small fraction of the cost. Installation,infrastructure and other equipment will dominate the costs. This isunlike computers and projectors where the product price is dominated bythe cost of CPU and the LCD respectively.

Number of Pixels

If a small LCOS device is required, the area can be halved to 13.2×13.2mm. This device (mLOIS) would have the same loss by keeping pixel sizeand pixel pitch the same but half the output ports because of thedecreased number of pixels. If even smaller active area is desired, a9.1×9.1 mm active area would introduce the same losses but with aquarter of the users. The smallest device to consider has a 2.9×2.9 mmactive area. It would still have an acceptable number of users and withlow cost. Below this size, there will be no substantial cost benefit andthe optical design would become complex due to the small size.

Output Ports

When single mode fibres are used for output ports, their outer diameteris D_(Fo)=125 μm and the core diameter is d_(Fo)=10 μm (see FIG. 3). Thebeam width on the device is such that 2w_(d)/L=0.4. For the proposedLOIS chip, N=1024, L=18.4 mm. The value of α is chosen so that thedesired trade off between efficiency and the number of output ports isachieved. For α=0.17 there are 112 output ports available while withα=0.59 there are 390 output ports. For FIG. 3, where there are 192ports, α=0.30.

The number of ports may be increased or the active area of the LCOSdevice may be decreased by using a MMF, a taper fibre of a micro-lens infront of a SMF instead of just a SMF. For a short span network, like asmall neighbourhood or a large building, where the fibres are only a fewhundred meters long, MMF may provide the required bandwidth but withlower cost. When using a MMF, the core is substantially bigger comparedwith a SMF, 62.5 μm instead of 10 μm. However, the input fibre willremain a SMF with a small core. For the beam of the SMF to match the MMFcore, the output plane should be optically magnified while, the spacingof the fibres will remain the same. The result is that more MMF fibrescan be placed on the output plane or a smaller device may be used withfewer pixels. If the ratio

$\left( \frac{d_{Fo}}{D_{Fo}} \right)$

increases by a factor of ×6.25 a similar decrease can occur at N.Therefore the number of pixels can be decreased from 1024 to 164 pixelswith an active area of 2.9×2.9 mm and the capabilities of the system interms of port count and loss will remain as in Table 1.

TABLE 1 The total losses for the LOIS device taking two scenarios: whentotal loss is −5.2 dB (α = 0.59) and when the total loss is −3.2 dB. (α= 0.17). The number of ports corresponds to a SMF used in the output andincreases by a factor of imes6.25² if MMFs are used. Loss α = 0.59 α =0.17 390 112 ports ports Apodisation −0.1 dB −0.1 dB Fill Factor −0.2 dB−0.2 dB Hologram −0.9 dB −0.9 dB Phase Quantisation −0.0 dB −0.0 dB Sincenvelope + −1.6 dB −0.6 dB Fringing fields (max - 3.2 dB) (max - 1.1 dB)Total loss −2.8 dB −1.8 dB (max - 4.4 dB) (max - 2.3 dB)

Efficiency

Some of the system losses are affected by the number of output ports andsome not. All the factors affecting system efficiency are shown inTable 1. Apodisation and fill factor incur the same losses to theinterconnect irrespective of the number of output ports (see section 1and 2). Unlike, the hologram efficiency (section 3 and FIG. 7) isrelated to the number of output ports. The number of output ports, S isnot known so the worst case scenario is considered which is −0.9 dB. Thephase quantisation when 5-bits per pixel are used is negligible and canbe easily ignored (see FIG. 11). Finally, the sinc envelope attenuationand the fringing field losses should be considered together. The worstcase scenario is when the beam is deflected for a maximum angle. Forα=0.59 this attenuation is −3.2 dB while for α=0.17 the attenuation is−1.1 dB. The mean value of loss, which could be more appropriate wasalso calculated and shown in Table 1. Note that high loss fibres (e.g.long distance between interconnect and subscriber) should be placedtowards the centre of the output plane and low loss links on the outerregions. Adding all the losses together, the overall mean efficiency ofthe system is −1.8 dB if there are 112 ports and −2.8 dB if there are390 ports. Loss could also be seen as a reduction in the number ofusers. If the laser source of the system had just enough power for allthe output ports, by reducing efficiency the number of users alsodecreases.

Example System

The final system will depend on the needs of the network. Number ofmaximum users, S_(max), cost and power available (and thus efficiency)are the three parameters that will determine the characteristics of theLCOS chip. Once the number of users is decided, the relationship betweenloss (α) and the number of pixels (N) is determined. Increasing thenumber of pixels while keeping the number of users the same willincrease the active area L×L and thus the cost of the device. At thesame time a decreases and so do the losses.

The first proposed system will use the LOIS device. Such a device couldbe used for the backbone of a HDTV distribution system. The input to theswitch will be a SMF connected to a laser operating at 1.5 μm or 1.3 μm.It will require less than 100 ports and low losses. Possibly at anypoint only 10 to 20 outputs are connected thus the power at the outputfibres remains high but the system retains the capability to shift thepower to any output in case of a link failure.

The second proposed system will also have as input a SMF connected to alaser. However, this system will be used within a neighbourhood and theoutput ports will have larger diameter (MMF, taper fiber or a SMF with amicro-lens). A 850 nm laser can be used too. The number of users perneighbourhood will be more than 100 and all of them may be connected.The cost of the device will be more important factor as more of thesedevices will be deployed so smaller LCOS devices will be used. The nLOISdevice can be used with loss of −2.8 dB to −4.4 dB and with about 390ports (α=0.59 in Table 1).

If necessary, a VCSEL may be used as an input to the interconnect. AsVCSELS have larger beam width than a laser, the required magnificationwill be less than ×6.25 when used with SMF. This effectively reduces thenumber of ports. Devices like them LOIS and μLOIS may be used in thiscases when the output ports are MMF and the input is a VCSEL. Also, ifthe fibre grid has a spacing of 250 μm instead of 125 μm, the number ofoutput ports will also decrease by a factor of four. Fibre ribbons with250 μm spacing are widely available. Again the mLOIS and μLOIS deviceswith more pixels can provide the necessary port count for a switch thatuses MMF for outputs.

We have thus investigated the use of LCOS devices for multicastingoptical interconnects. Mathematical formulae to link the characteristicsof the system—efficiency, number of output ports, pixel number anddevice area—were presented. This enables the optical engineer to bestuse the resources of the device. A number of devices were presented andit was found that even very small devices with active area of only 9 mm²can be used for multicasting optical signals. Larger devices with areasup to 339 mm² can be used for distributing signals to SMF with very lowloss. The number of output ports and thus subscribers is large with morethan 100's ports per switch. It can be further increased by enlargingthe diameter of the output ports.

Concluding, LCOS devices could be the way to multicast optical signalsto the house in the near future. Their cost, flexibility, reliabilityand large number of output ports make them the ideal solution. As thepower of lasers increases and similarly the bandwidth requirementsincrease, it becomes clear that performing the signal distribution inthe optical domain is important and LCOS devices can do that in a veryeffective way.

Embodiments techniques we have described may also in principle beapplied to liquid crystal spatial light modulators other than when inthe form of an LCOS SLM. No doubt many other effective alternatives willoccur to the skilled person. It will be understood that the invention isnot limited to the described embodiments and encompasses modificationsapparent to those skilled in the art lying within the scope of theclaims appended hereto.

1. An LCOS (liquid crystal on silicon) telecommunications light beamrouting device, the device comprising: an optical input; a plurality ofoptical outputs; a LCOS spatial light modulator (SLM) in an optical pathbetween said input and said output, for displaying a kinoform; a dataprocessor, coupled to said SLM, configured to provide kinoform data fordisplaying said kinoform on said SLM; wherein said kinoform data definesa kinoform which routes a beam from said optical input to a selectedsaid optical output; wherein said data processor is configured to inputrouting data defining said selected optical output and to calculate saidkinoform data for routing said beam responsive to said routing data; andwherein said data processor is configured to calculate said kinoformdata by: determining an initial phase pattern for said kinoform;calculating a replay field of said phase pattern; modifying an amplitudecomponent of said replay field to represent a target replay field forsaid beam routing, retaining a phase component of said replay field toprovide an updated replay field; performing a space-frequency transformon said updated replay field to determine an updated phase pattern forsaid kinoform; and repeating said calculating and updating of saidreplay field and said performing of said space-frequency transform untilsaid kinoform for display is determined; and outputting said kinoformdata for display on said LCOS SLM. 2-10. (canceled)
 11. A method ofoptical telecommunications light beam routing, the method comprising:displaying a kinoform on an LCOS SLM; providing an input light beam tosaid LCOS SLM; and diffracting said light beam with said kinoform toprovide a diffracted output beam from said LCOS SLM; the method furthercomprising: calculating said kinoform displayed on said SLM using aping-pong algorithm. 12-15. (canceled)